Simplify the following expression: $ r = \dfrac{-7}{4} + \dfrac{3y}{y - 3} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y - 3}{y - 3}$ $ \dfrac{-7}{4} \times \dfrac{y - 3}{y - 3} = \dfrac{-7y + 21}{4y - 12} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{3y}{y - 3} \times \dfrac{4}{4} = \dfrac{12y}{4y - 12} $ Therefore $ r = \dfrac{-7y + 21}{4y - 12} + \dfrac{12y}{4y - 12} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-7y + 21 + 12y}{4y - 12} $ $r = \dfrac{5y + 21}{4y - 12}$